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These are the first five terms in a Fibonacci sequence - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Question 11
These are the first five terms in a Fibonacci sequence. 1 3 4 7 11 Write down the next two terms in the sequence. In a different Fibonacci sequence the fourth... show full transcript
Worked Solution & Example Answer:These are the first five terms in a Fibonacci sequence - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Step 1
Step 2
Work out the first term in this sequence.
Answer
Let the first term be denoted as 'a'. In this Fibonacci sequence:
- The fourth term is 31, which can be written as x + y = 31.
- The fifth term is 50, which can be written as y + (x + y) = 50 or x + 2y = 50.
Now we can solve these equations:
- From the first equation:
- We have x + y = 31.
- From the second equation:
- We transform it to get: x + 2y = 50.
Subtracting the first equation from the second yields:
- (x + 2y) - (x + y) = 50 - 31
- This simplifies to: y = 19.
Substituting y back into the first equation gives:
- x + 19 = 31
- Therefore, x = 31 - 19 = 12.
Thus, the first term is 7.
Step 3
Write down algebraic expressions for the first, fourth and fifth terms.
Answer
Given the second and third terms are x and y,
- The first term can be expressed as: First term = y - x.
- The fourth term expression is: Fourth term = x + y.
- The fifth term expression is: Fifth term = x + 2y.
In summary:
- First term = y - x
- Fourth term = x + y
- Fifth term = x + 2y